Rhombus calculation

Description for the calculation of a rhombus

Raute berechnen

A rhombus is a quadrangular geometric shape and has the following characteristics

  • All four sides are the same length

  • The angles of the opposite corners are identical

  • The opposite sides are parallel to each other


\(a\)   Length

\(h\)   Height

\(A\)   Area

\(P\)   Perimeter

\(e\)   Long diagonal

\(f\)   Short diagonal

\( α\)   Angle Alpha

\( β\)   Angle Beta

Formulas for rhombus calculation

Calculate Area \(A\) of a rhombus

\(A = a · h\)

\(\displaystyle A= \frac{e · f}{2}\)

\(A=a2 · sin(α)\)

Calculate Length \(a\) of a rhombus

\(a = A / h\)

\(\displaystyle a = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2}\)

Calculate Height \(h\) of a rhombus

\(\displaystyle h = \frac{A}{a}\)

\(h = sin(α) · a\)

\(b = sin(β) · a\)

Calculate Perimeter \(P\) of a rhombus

\(P = 4 · a\)

\(\displaystyle P = 4 · \frac{h}{sin(α)}\)

\(\displaystyle P = 4 · \frac{h}{sin(β)}\)

Calculate long Diagonal \(e\) of a rhombus

\(\displaystyle e =\frac{ h }{ sin(α/2)}\)

\(\displaystyle e = a ·\frac{ sin(β)}{ sin(α/2)}\)

\(\displaystyle e = 2 · a · cos\left(\frac{α}{2}\right)\)

Calculate short Diagonal \(f\) of a rhombus

\(\displaystyle f =\frac{ h }{ sin(β/2)}\)

\(\displaystyle f = a ·\frac{ sin(α)}{ sin(β/2)}\)

\(\displaystyle f = 2 · a · cos\left(\frac{β}{2}\right)\)

Calculate Angle Beta \(β\) of a rhombus

\(\displaystyle β =\frac{asin( h) }{a}\)